A particle executes simple harmonic motion under the restoring force provided by a spring.

Monjur Alahi

A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is T. If the spring is divided in two equal parts and one part is used to continue the simple harmonic motion, the time period will

(a) remain T  

(b) become 2T

(c) become T/2

(d) become T/√2.


0 like 0 dislike
1 views
Share with your friends

1 Answers

Salim Ahmed Kawsar

Call

(d) become T/√2.

EXPLANATION:  

The time period of a spring-mass system is given as T = 2π√(m/k). 

When the spring is divided in two equal halves the spring constant of each half doubles, so k'=2k. 

New time period T'=2π√{m/(2k)}=(1/√2)*2π√(m/k) T/√2. Hence the option (d).  

0 like 0 dislike
1 views
Talk Doctor Online in Bissoy App
A body executes simple harmonic motion.

(a) : Kinetic energy is maximum at x = 0.

1 Answers 1 views
A student says that he had applied a force F = k√x on a particle and the particle moved in simple harmonic motion.

(a) As x increases k increases.  Explanation: Since the motion is simple harmonic, the force F=-⍵²x where ⍵² is a constant. Equating the force applied by the student we get, -k/x=-⍵²x  →k=⍵²x²  It is...

1 Answers 1 views
The time period of a particle in simple harmonic motion is equal to the time between consecutive .

(b) an extreme position  EXPLANATION:  At the extreme position the particle is in the same phase at consecutive appearance, hence (b) is true. In all other options, the consecutive appearance of the...

1 Answers 1 views
The displacement of a particle in simple harmonic motion in one time period is

The correct answer is (d) zero. EXPLANATION:   The displacement is a vector and its magnitude is given by the line joining the initial position to the final position. Since after one time period...

1 Answers 1 views
particle moves on the X-axis according to the equation x = A + B sincot. The motion is simple harmonic with amplitude

The correct answer is (b) B EXPLANATION: The equation can be written as x-A=B.sin⍵t If x-A=y then y=B.sin⍵t This is the equation of a simple harmonic motion with amplitude B. Hence option(b). 

1 Answers 1 views
The total mechanical energy of a spring-mass system in simple harmonic motion is E =1/2 m ω^2 A^2 Suppose

(d) remain E. EXPLANATION:   Since no external work is done on the system the energy of the system will remain the same. Hence option (d).   

1 Answers 1 views
A particle executes simple harmonic motion with a frequency v. The frequency with which the kinetic energy oscillates is

The correct answer is (c) 2 v EXPLANATION:  Between one extreme position to another i.e. in half the time period the K.E. increases from zero to maximum (at the mean position) and again...

1 Answers 1 views
For a particle executing simple harmonic motion, the acceleration is proportional to

(a) displacement from the mean position EXPLANATION:   Since a=-⍵²x, where x is the shortest instantaneous distance from the mean position i.e. magnitude of the displacement from the mean position. Hence (a) is...

1 Answers 1 views
A cork floating in a calm pond executes simple harmonic motion of frequency v when a wave generated by a boat passes by it.

The correct answer is (a) v EXPLANATION:  The time taken by the wave in moving one wavelength is exactly the same as in moving the cork one oscillation. Hence the frequency of...

1 Answers 1 views
The total mechanical energy of a spring-mass system in simple harmonic motion is E = 1/2mω^2A^2.

(d) remain E. EXPLANATION:   Since no external work is done on the system the energy of the system will remain the same. Hence option (d).   

1 Answers 1 views
X